Single-Clicking the spreadsheet in the drawing will select it and present grab handles at the corner for resizing. However, this only scales your view. It does NOT change the portion of the spreadsheet that is viewable.

SW2013 SP3 does not seem to provide an obvious method to modify the viewable cells shown in the drawing.

I am trying to do this as well but find that often a portion of what I am pasting into Solidworks does not show. I can't seem to change the extent of how much data is shown in Solidworks, it simply changes the scaling of the data in Solidwork instead of expanding the amount of data shown. Do you have this issue? Have to got a work around?

SW has always functioned a bit oddly with inserted spreadsheets. When you insert a spreadsheet (Insert / Object / created from file) frame around the inserted worksheet will indeed just scale the inserted object. You need to double-click the inserted worksheet to switch in to edit mode. In this mode you can drag the border (just like discussed above) and this time the view will not scale. Once you have the area of the worksheet showing as you desire click anywhere outside of the worksheet window to exit the edit mode. Your inserted worksheet should now show up just as you edited it.

I have tried the procedure you suggested, however, it does not re-size correctly.

The image below shows the data I selected to copy from excel

The image below shows the result of the paste into Solidworks. (Notice that Right hand side of content is not showing)

The result after trying to expand the window. I double clicked in the excel data to activate it and then re-sized the window while it was activated. After re-sizing and then clicking out of the excel data the result is what you see below.

That is what I tried to do but my result was not the same as yours. I will try again but fear I may have no luck. Others who I currently work with have said this is an issue they have had for many years with no luck on a solution so far.

If you need to have the spread sheet linked, then what you would need to do to have additional cells show is delete the original and insert the updated spread sheet with the added columns. I expect you would need to do this every time you added or deleted columns.